diff --git a/include/clad/Differentiator/DiffPlanner.h b/include/clad/Differentiator/DiffPlanner.h
index fe37046c4..663b24b47 100644
--- a/include/clad/Differentiator/DiffPlanner.h
+++ b/include/clad/Differentiator/DiffPlanner.h
@@ -47,7 +47,7 @@ struct DiffRequest {
   /// Args provided to the call to clad::gradient/differentiate.
   const clang::Expr* Args = nullptr;
   /// Indexes of global GPU args of function as a subset of Args.
-  std::unordered_set<size_t> GlobalArgsIndexes;
+  std::vector<size_t> GlobalArgsIndexes;
   /// Requested differentiation mode, forward or reverse.
   DiffMode Mode = DiffMode::unknown;
   /// If function appears in the call to clad::gradient/differentiate,
diff --git a/lib/Differentiator/ReverseModeVisitor.cpp b/lib/Differentiator/ReverseModeVisitor.cpp
index 4af15553e..69123df5c 100644
--- a/lib/Differentiator/ReverseModeVisitor.cpp
+++ b/lib/Differentiator/ReverseModeVisitor.cpp
@@ -563,6 +563,8 @@ Expr* getArraySizeExpr(const ArrayType* AT, ASTContext& context,
 
     auto derivativeName =
         utils::ComputeEffectiveFnName(m_DiffReq.Function) + "_pullback";
+    for (auto index : m_DiffReq.GlobalArgsIndexes)
+      derivativeName += "_" + std::to_string(index);
     auto DNI = utils::BuildDeclarationNameInfo(m_Sema, derivativeName);
 
     auto paramTypes = ComputeParamTypes(args);
@@ -1929,6 +1931,7 @@ Expr* getArraySizeExpr(const ArrayType* AT, ASTContext& context,
     // If it has more args or f_darg0 was not found, we look for its pullback
     // function.
     const auto* MD = dyn_cast<CXXMethodDecl>(FD);
+    std::vector<size_t> globalCallArgs;
     if (!OverloadedDerivedFn) {
       size_t idx = 0;
 
@@ -1994,12 +1997,23 @@ Expr* getArraySizeExpr(const ArrayType* AT, ASTContext& context,
                                 pullback);
 
       // Try to find it in builtin derivatives
+      std::string customPullback =
+          clad::utils::ComputeEffectiveFnName(FD) + "_pullback";
+      // Add the indexes of the global args to the custom pullback name
+      if (!m_GlobalArgs.empty())
+        for (size_t i = 0; i < pullbackCallArgs.size(); i++)
+          if (auto* DRE = dyn_cast<DeclRefExpr>(pullbackCallArgs[i]))
+            if (auto* param = dyn_cast<ParmVarDecl>(DRE->getDecl()))
+              if (m_GlobalArgs.find(param) != m_GlobalArgs.end()) {
+                customPullback += "_" + std::to_string(i);
+                globalCallArgs.emplace_back(i);
+              }
+
       if (baseDiff.getExpr())
         pullbackCallArgs.insert(
             pullbackCallArgs.begin(),
             BuildOp(UnaryOperatorKind::UO_AddrOf, baseDiff.getExpr()));
-      std::string customPullback =
-          clad::utils::ComputeEffectiveFnName(FD) + "_pullback";
+
       OverloadedDerivedFn =
           m_Builder.BuildCallToCustomDerivativeOrNumericalDiff(
               customPullback, pullbackCallArgs, getCurrentScope(),
@@ -2035,12 +2049,7 @@ Expr* getArraySizeExpr(const ArrayType* AT, ASTContext& context,
 
         // Mark the indexes of the global args. Necessary if the argument of the
         // call has a different name than the function's signature parameter.
-        if (!m_GlobalArgs.empty())
-          for (size_t i = 0; i < pullbackCallArgs.size(); i++)
-            if (auto* DRE = dyn_cast<DeclRefExpr>(pullbackCallArgs[i]))
-              if (auto* param = dyn_cast<ParmVarDecl>(DRE->getDecl()))
-                if (m_GlobalArgs.find(param) != m_GlobalArgs.end())
-                  pullbackRequest.GlobalArgsIndexes.emplace(i);
+        pullbackRequest.GlobalArgsIndexes = globalCallArgs;
 
         pullbackRequest.BaseFunctionName =
             clad::utils::ComputeEffectiveFnName(FD);
diff --git a/test/CUDA/GradientKernels.cu b/test/CUDA/GradientKernels.cu
index 5d8d1696a..70ecd96c0 100644
--- a/test/CUDA/GradientKernels.cu
+++ b/test/CUDA/GradientKernels.cu
@@ -308,7 +308,7 @@ __global__ void kernel_with_device_call(double *out, double *in, double val) {
 //CHECK-NEXT:        _d_out[index0] = 0.;
 //CHECK-NEXT:        double _r0 = 0.;
 //CHECK-NEXT:        double _r1 = 0.;
-//CHECK-NEXT:        device_fn_pullback(in[index0], val, _r_d0, &_r0, &_r1);
+//CHECK-NEXT:        device_fn_pullback_1(in[index0], val, _r_d0, &_r0, &_r1);
 //CHECK-NEXT:        atomicAdd(_d_val, _r1);
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
@@ -323,6 +323,11 @@ __global__ void kernel_with_device_call_2(double *out, double *in, double val) {
   out[index] = device_fn_2(in, val);
 } 
 
+__global__ void dup_kernel_with_device_call_2(double *out, double *in, double val) {
+  int index = threadIdx.x;
+  out[index] = device_fn_2(in, val);
+} 
+
 // CHECK: void kernel_with_device_call_2_grad_0_2(double *out, double *in, double val, double *_d_out, double *_d_val) {
 //CHECK-NEXT:    int _d_index = 0;
 //CHECK-NEXT:    int index0 = threadIdx.x;
@@ -333,7 +338,7 @@ __global__ void kernel_with_device_call_2(double *out, double *in, double val) {
 //CHECK-NEXT:        double _r_d0 = _d_out[index0];
 //CHECK-NEXT:        _d_out[index0] = 0.;
 //CHECK-NEXT:        double _r0 = 0.;
-//CHECK-NEXT:        device_fn_2_pullback(in, val, _r_d0, &_r0);
+//CHECK-NEXT:        device_fn_2_pullback_0_1(in, val, _r_d0, &_r0);
 //CHECK-NEXT:        atomicAdd(_d_val, _r0);
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
@@ -349,7 +354,7 @@ __global__ void kernel_with_device_call_2(double *out, double *in, double val) {
 //CHECK-NEXT:        double _r_d0 = _d_out[index0];
 //CHECK-NEXT:        _d_out[index0] = 0.;
 //CHECK-NEXT:        double _r0 = 0.;
-//CHECK-NEXT:        device_fn_2_pullback(in, val, _r_d0, _d_in, &_r0);
+//CHECK-NEXT:        device_fn_2_pullback_0_1_3(in, val, _r_d0, _d_in, &_r0);
 //CHECK-NEXT:        _d_val += _r0;
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
@@ -373,7 +378,7 @@ __global__ void kernel_with_device_call_3(double *out, double *in, double *val)
 //CHECK-NEXT:        out[index0] = _t0;
 //CHECK-NEXT:        double _r_d0 = _d_out[index0];
 //CHECK-NEXT:        _d_out[index0] = 0.;
-//CHECK-NEXT:        device_fn_3_pullback(in, val, _r_d0, _d_in, _d_val);
+//CHECK-NEXT:        device_fn_3_pullback_0_1_3_4(in, val, _r_d0, _d_in, _d_val);
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
 
@@ -402,19 +407,19 @@ __global__ void kernel_with_nested_device_call(double *out, double *in, double v
 //CHECK-NEXT:       double _r_d0 = _d_out[index0];
 //CHECK-NEXT:        _d_out[index0] = 0.;
 //CHECK-NEXT:        double _r0 = 0.;
-//CHECK-NEXT:        device_with_device_call_pullback(in, val, _r_d0, _d_in, &_r0);
+//CHECK-NEXT:        device_with_device_call_pullback_0_1_3(in, val, _r_d0, _d_in, &_r0);
 //CHECK-NEXT:        _d_val += _r0;
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
 
-// CHECK: __attribute__((device)) void device_fn_pullback(double in, double val, double _d_y, double *_d_in, double *_d_val) {
+// CHECK: __attribute__((device)) void device_fn_pullback_1(double in, double val, double _d_y, double *_d_in, double *_d_val) {
 //CHECK-NEXT:    {
 //CHECK-NEXT:                *_d_in += _d_y;
 //CHECK-NEXT:                *_d_val += _d_y;
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
 
-// CHECK: __attribute__((device)) void device_fn_2_pullback(double *in, double val, double _d_y, double *_d_val) {
+// CHECK: __attribute__((device)) void device_fn_2_pullback_0_1(double *in, double val, double _d_y, double *_d_val) {
 //CHECK-NEXT:    unsigned int _t1 = blockIdx.x;
 //CHECK-NEXT:    unsigned int _t0 = blockDim.x;
 //CHECK-NEXT:    int _d_index = 0;
@@ -422,7 +427,7 @@ __global__ void kernel_with_nested_device_call(double *out, double *in, double v
 //CHECK-NEXT:    *_d_val += _d_y;
 //CHECK-NEXT:}
 
-// CHECK: __attribute__((device)) void device_fn_2_pullback(double *in, double val, double _d_y, double *_d_in, double *_d_val) {
+// CHECK: __attribute__((device)) void device_fn_2_pullback_0_1_3(double *in, double val, double _d_y, double *_d_in, double *_d_val) {
 //CHECK-NEXT:    unsigned int _t1 = blockIdx.x;
 //CHECK-NEXT:    unsigned int _t0 = blockDim.x;
 //CHECK-NEXT:    int _d_index = 0;
@@ -433,7 +438,7 @@ __global__ void kernel_with_nested_device_call(double *out, double *in, double v
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
 
-// CHECK: __attribute__((device)) void device_fn_3_pullback(double *in, double *val, double _d_y, double *_d_in, double *_d_val) {
+// CHECK: __attribute__((device)) void device_fn_3_pullback_0_1_3_4(double *in, double *val, double _d_y, double *_d_in, double *_d_val) {
 //CHECK-NEXT:    unsigned int _t1 = blockIdx.x;
 //CHECK-NEXT:    unsigned int _t0 = blockDim.x;
 //CHECK-NEXT:    int _d_index = 0;
@@ -444,7 +449,7 @@ __global__ void kernel_with_nested_device_call(double *out, double *in, double v
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
 
-// CHECK: __attribute__((device)) void device_with_device_call_pullback(double *in, double val, double _d_y, double *_d_in, double *_d_val) {
+// CHECK: __attribute__((device)) void device_with_device_call_pullback_0_1_3(double *in, double val, double _d_y, double *_d_in, double *_d_val) {
 //CHECK-NEXT:    {
 //CHECK-NEXT:        double _r0 = 0.;
 //CHECK-NEXT:        device_fn_4_pullback(in, val, _d_y, _d_in, &_r0);
@@ -452,7 +457,7 @@ __global__ void kernel_with_nested_device_call(double *out, double *in, double v
 //CHECK-NEXT:    }
 //CHECK-NEXT:}
 
-// CHECK: __attribute__((device)) void device_fn_4_pullback(double *in, double val, double _d_y, double *_d_in, double *_d_val) {
+// CHECK: __attribute__((device)) void device_fn_4_pullback_0_1_3(double *in, double val, double _d_y, double *_d_in, double *_d_val) {
 //CHECK-NEXT:    unsigned int _t1 = blockIdx.x;
 //CHECK-NEXT:    unsigned int _t0 = blockDim.x;
 //CHECK-NEXT:    int _d_index = 0;
@@ -690,6 +695,15 @@ int main(void) {
 
   INIT(dummy_in_double, dummy_out_double, val, d_in_double, d_out_double, d_val);
 
+  auto check_dup = clad::gradient(dup_kernel_with_device_call_2, "out, val"); // check that the pullback function is not regenerated
+  check_dup.execute_kernel(dim3(1), dim3(10, 1, 1), dummy_out_double, dummy_in_double, 5, d_out_double, d_val);
+  cudaMemcpy(res, d_val, sizeof(double), cudaMemcpyDeviceToHost);
+  cudaDeviceSynchronize();
+  printf("%s\n", cudaGetErrorString(cudaGetLastError())); // CHECK-EXEC: no error
+  printf("%0.2f\n", *res); // CHECK-EXEC: 50.00
+
+  INIT(dummy_in_double, dummy_out_double, val, d_in_double, d_out_double, d_val);
+
   auto test_device_3 = clad::gradient(kernel_with_device_call_2, "out, in");
   test_device_3.execute_kernel(dim3(1), dim3(10, 1, 1), dummy_out_double, dummy_in_double, 5, d_out_double, d_in_double);
   cudaDeviceSynchronize();